In the process of shock-wave reflection at a surface, a transition from regular to Mach reflection occurs when the angle of incidence exceeds a certain critical value. This critical angle, which depends on the Mach number of the propagating shock wave and γ, the adiabatic exponent of the medium, is well approximated in many experimental situations by its value in the limit of infinite Mach number. Unfortunately, the often-cited critical angle for infinitely strong shock waves is incorrect. We present a short analysis of the process of shock-wave reflection and discuss the condition for infinitely strong shock waves. The exact and approximate solutions for the dependence of the critical angle on the adiabatic exponent of the medium are also compared with the above-mentioned formula.

Analytical forms for the short-range correlations present at the surface of a multiple-scattering medium are derived from diffusion theory.

We report numerical studies of the ‘‘memory-loss’’ phase transition in Hopfield-like symmetric neural networks in which the neurons are connected to all other neurons within a local neighborhood (dense, short-range connectivity). The number of connections per neuron K scales as the number of neurons N raised to a power less than 1 (i.e., K∼${\mathit{N}}^{\mathrm{\eta }}$, η<1). We use the recently developed Lee-Kosterlitz finite-size scaling technique to determine the critical value of η below which the first-order phase transition disappears.

Time-dependent wave-packet theory is formulated for fairly-low-energy elastic electron scattering. The Schrödinger equation is solved numerically in the time and two spatial dimensions for e-He scattering in the static–local-exchange approximation. The angular distribution is calculated from a single pass through the region of the target and shows good agreement with the angular distribution calculated with knowledge of the phase shifts from the solution of the set of time-independent radial equations.

A procedure is presented for calculations of double-perturbation problems in the coupled-cluster formalism. With use of this method to include to all orders the correlation effects of single and pair excitations, the enhancement factor R=-585 is obtained for the electric dipole moment (EDM) in atomic thallium. Equations for EDM perturbed single-excitation amplitudes are solved by diagonalization to take into account mixing between excited core states, and perturbed pair functions are introduced to incorporate correlation effects. Considering contributions from higher-order perturbation terms, we estimate the accuracy of the obtained enhancement factor is approximately at the 5–10 % level.

We have used the coupled-channel method to study the significance of electron correlation in the reaction mechanism for two-electron capture in ${\mathrm{C}}^{5+}$-He collisions. Two different sets of calculations were performed. While the static correlation energy was generally included in the calculations, further correlation effects were ignored in the first set of calculations. In the second set of calculations the so-called doubly excited symmetry basis (DESB) states were used to model the spatial electron correlation. The difference between the two sets of results is so profound that we can conclude that electron correlation plays an essential role in the reaction mechanism. The results of the DESB-based calculations are in good agreement with experimental data [Holt et al., Phys. Rev. A 43, 607 (1991)].

Total cross sections for single-electron capture from He by keV ${\mathrm{O}}^{+}$ ${}_{}{}^2{}_{}{}^{}$D° and ${}_{}{}^2{}_{}{}^{}$P° metastable ions turned out to be much smaller than for ${\mathrm{O}}^{+}$ ${}_{}{}^4{}_{}{}^{}$S° ground state ions, despite a larger energy defect for the latter reaction. We suggest that this unexpected behavior is caused by efficient suppression of electron capture into either metastable ion due to a competing, collisionally induced inelastic transition into the companion metastable state.

We show by calculation that for a mixture of nonreacting gases the electronic stopping cross section at low projectile velocities may deviate from the weighted mean of the single-component values (Bragg’s rule). This departure is significant if the individual cross sections for electron capture and electron loss differ considerably. In this case, mixing not only changes the mean charge state in a nonlinear way, but also speeds up the charge-changing cycle. For stopping of 4-keV hydrogen projectiles in a mixture of helium and hydrogen gas, we find that energy losses due to charge-changing processes differ by a factor of 2 from simple additivity. The stopping cross section will be about 50% larger than the result obtained from Bragg’s rule.

A nonlinear system with delayed feedback, whenever the delay time is much longer than the intrinsic correlation time, displays two widely separated time scales. In such a case, a two-dimensional representation becomes appropriate, because it discloses features otherwise hidden in the one-dimensional sequence of data, and allows use of recognition algorithms developed for spatiotemporal chaos. As an illustration, chaotic time sequences from a single-mode laser with delayed feedback are analyzed using this representation.

We present an alternative method for studying excitation of atoms in intense laser fields. In the present paper we focus upon the optical harmonic generation by hydrogen atoms.

Enhancement of greater than 2 orders of magnitude of nonresonant third-harmonic generation from an optically pumped ${\mathit{S}}_1$ electronic excited state is experimentally observed for quasi-two-dimensional conjugated disklike structures. The isotropically averaged ${\mathit{S}}_1$ excited-state microscopic susceptibility 〈${\gamma }_1^{\mathit{S}}$(-3ω;ω,ω,ω)〉 is -1640±100×${10}^{\mathrm{-}36}$ esu, and the corresponding macroscopic ${\mathrm{\chi }}_{\mathit{S}1}^{\mathrm{}\left(3\right)\mathrm{}}$(-3ω;ω,ω,ω) exhibits temporal decay and pump-power saturation behavior associated with the expected decay and saturation of the ${\mathit{S}}_1$ state. The enhancement mechanism through optical pumping followed by a nonresonant nonlinear optical probe is generalizable to both second- and third-order optical processes in nonlinear optical media.

We report the observation of transverse optical bistability (TOB) in a sodium-filled Fabry-Pérot resonator, pumped by circularly polarized light, nearly resonant with the ${\mathit{D}}_1$ line, in the presence of a buffer gas, for low vapor density. A sequence of circularly symmetric patterns, ascribable to superpositions of resonator modes, is obtained. The appearance of TOB can be explained in terms of a self-induced intensity-dependent lens formed in the medium by the interaction with the laser light. A simple model that considers the transverse diffusion of the atoms inside the cell provides predictions in good qualitative agreement with the observations.

We propose a unifying picture of d-dimensional diffusion in randomly correlated media ż(x,t)=DΔz+V(x)z using the replica-scaling method of Zhang [Phys. Rev. B 42, 4897 (1990)]. Here V(x) denotes a frozen random potential of strength λ and correlation length a and arbitrary variance 〈V(x)V(0)〉=${\lambda }^2$${\mathit{R}}_{\mathit{a}}$(x). We are interested in the temporal dependence of 〈${\mathit{Z}}^{\mathit{n}}$〉 and the diffusion law. It is demonstrated, in particular, that for the special case of uncorrelated disorder the asymptotic behavior is given by ln〈${\mathit{Z}}^{\mathit{n}}$〉≃${\lambda }^2$${\mathit{a}}^{\mathrm{-}\mathit{d}}$${\mathit{n}}^2$${\mathit{t}}^2$, recovering the earlier result of Zeldovich et al. [Sov. Phys. JETP 62, 1188 (1985)], whereas at intermediate times nt≤${\mathit{Da}}^{\mathit{d}\mathrm{-}2}$/${\lambda }^2$ the situation is dimension dependent: we obtain ln〈${\mathit{Z}}^{\mathit{n}}$〉≃(${\lambda }^4$/${\mathit{D}}^{\mathit{d}}$${)}^{1/\left(2\mathrm{-}\mathit{d}\right)}$ (nt${)}^{\left(4\mathrm{}\mathrm{-}\mathit{d}\right)/\left(2\mathrm{}\mathrm{-}\mathit{d}\right)}$ for d<2 and ln〈${\mathit{Z}}^{\mathit{n}}$〉≃-n for d>4. For 2<d<4 we conclude that ln〈${\mathit{Z}}^{\mathit{n}}$〉≃${\lambda }^2$${\mathit{D}}^{\mathrm{-}\mathit{d}/2\mathrm{}}$${\mathit{n}}^2$${\mathit{t}}^{2\mathrm{-}(\mathit{d}/2)}$ if t<${\mathit{a}}^2$/D. The relation between the temporal dependence of 〈${\mathit{Z}}^{\mathit{n}}$〉 and the diffusion law is also established. These results are expected to be as accurate as other Flory-like theories.

We have studied avalanchelike rearrangements of domain patterns in the two-dimensional Ising model with static impurities, which is quenched to low temperatures. When breaking the up-down symmetry of the spins by a small applied field, the mere fluctuation of a single spin eventually results in a cascade of spin flips at the domain boundaries. We have analyzed the lifetime and size distribution functions for the avalanches and related the results to the general phenomena of self-organized criticality and to recent experiments on cellular magnetic domain patterns in magnetic garnet films. Our results suggest that the self-organized state in this system appears to be subcritical, in agreement with a recent theory.

We study the critical properties of a self-avoiding walk on percolation clusters using exact enumerations, in both d=2 and 3. Calculations of the exponent χ, which measures free-energy fluctuations, clearly show the existence of two distinct phases, one for strong disorder (at the percolation threshold), the other for weak disorder (above the percolation threshold). The ν exponent is, within numerical accuracy, the same in the two phases. However in d=3, its value, ν=0.64±0.015 is significantly larger than on a pure lattice.

It is known that the Frisch-Hasslacher-Pomeau lattice-gas automaton model and related models possess some rather unphysical effects. These are (1) a non-Galilean invariance caused by a density-dependent coefficient in the convection term, and (2) a velocity-dependent equation of state. In this paper, we show that both of these effects can be eliminated exactly in a lattice Boltzmann-equation model.

The gel point is a continuous transition between fluid and solid states, and therefore exhibits a variety of scaling laws for the linear viscoelastic behavior. These are derived, together with a scaling law for the nonlinear shear relaxation modulus and a sum rule, valid in both fluid and solid states, which has a counterpart in superconductivity. Our results are generic consequences of both dynamic critical phenomena and spontaneous symmetry breaking, and therefore are not equivalent to some previous predictions, based on an analogy with percolation.

The results of molecular-dynamics studies of surface-tension-dominated spinodal decomposition of initially well-mixed binary fluids in the absence and presence of gravity are presented. The growth exponent for the domain size and the decay exponent of the potential energy of interaction between the two species with time are found to be 0.6±0.1, inconsistent with scaling arguments based on dimensional analysis.

The Clebsch form of the Euler equations provides an intuitive picture as to how the circulation constraints direct the spatial organization of vorticity and favor the formation of vortex sheets. Porous media convection models the basic mechanism and is also the simplest generalization of the inviscid Burgers equation that allows for an incompressible velocity field. The finite time singularities of the model are studied numerically. A related convection analog to the axisymmetric Euler equations is discussed for comparison.

We report molecular-dynamics simulations of the anisotropic diffusion of infinitely thin platelets in the nematic phase. Our simulations are used to distinguish between the predictions of two different theories. The first theory, based on a mapping of the nematic phase of ellipsoidal particles on the hard-sphere fluid, predicts that both the longitudinal and the transverse diffusion constants decrease monotonically with increasing density. This is in stark contrast to a scaling argument which suggests that the transverse diffusion constant of platelets in the nematic phase in fact diverges with increasing density. Our simulations support the scaling argument.